A partially hydrogenated unsaturated nitrile-conjugated diene copolymer is well known as a rubber having good heat-aging resistance, oil resistance and rancid gasoline resistance. To utilize these good characteristics and impart other characteristics to this rubber, proposals have heretofore been made wherein the copolymer is blended with other rubbers. Among the rubber blends, a blend thereof with an ethylene-propylene-diene copolymer (hereinafter abbreviated to "EPDM") is well known as a rubber composition having good heat-aging resistance, oil resistance and ozone resistance (Japanese Unexamined Patent Publication No. 58-40332, 61-40342, 61-283639 and 62-190241). However, the partially hydrogenated unsaturated nitrile-conjugated diene copolymer rubber and EPDM have greatly different solubility parameters and hence, when mixed together, it is almost impossible that they form a uniformly dispersed mixture. Further, these copolymer rubbers exhibit different rates of vulcanization. Therefore, properties of a vulcanized rubber from the composition of these copolymer rubbers are restricted. Especially, the constant-elongation fatigue properties are not satisfactory.